Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions
In this paper we have provided sufficient conditions to study semilocal and local convergence of the Stirling’s method. The method is used to find fixed points of nonlinear operator equation. We assume Lipschtiz continuity type conditions on the first Fréchet derivative of the operator but no contra...
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| Format: | Article |
| Language: | English |
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Sciendo
2018-07-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/awutm-2018-0007 |
| _version_ | 1818469185720680448 |
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| author | Argyros Ioannis K. Parida P.K. |
| author_facet | Argyros Ioannis K. Parida P.K. |
| author_sort | Argyros Ioannis K. |
| collection | DOAJ |
| description | In this paper we have provided sufficient conditions to study semilocal and local convergence of the Stirling’s method. The method is used to find fixed points of nonlinear operator equation. We assume Lipschtiz continuity type conditions on the first Fréchet derivative of the operator but no contractive conditions as in earlier works. This way expand the applicability of this method. Here we introduce a new type of majorizing sequences instead of usual majorizing sequences and recurrence relations. Finally the paper will be concluded with numerical examples and a favorable comparison with known results. |
| first_indexed | 2024-04-13T21:21:13Z |
| format | Article |
| id | doaj.art-b013218de8d445f3b987e52f7bad5615 |
| institution | Directory Open Access Journal |
| issn | 1841-3307 |
| language | English |
| last_indexed | 2024-04-13T21:21:13Z |
| publishDate | 2018-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annals of the West University of Timisoara: Mathematics and Computer Science |
| spelling | doaj.art-b013218de8d445f3b987e52f7bad56152022-12-22T02:29:29ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072018-07-01561869810.2478/awutm-2018-0007awutm-2018-0007Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence RegionsArgyros Ioannis K.0Parida P.K.1Department of Mathematical Sciences, Cameron University, Lawton, USACenter for Applied Mathematics, Central University of Jharkhand, Ranchi, IndiaIn this paper we have provided sufficient conditions to study semilocal and local convergence of the Stirling’s method. The method is used to find fixed points of nonlinear operator equation. We assume Lipschtiz continuity type conditions on the first Fréchet derivative of the operator but no contractive conditions as in earlier works. This way expand the applicability of this method. Here we introduce a new type of majorizing sequences instead of usual majorizing sequences and recurrence relations. Finally the paper will be concluded with numerical examples and a favorable comparison with known results.https://doi.org/10.2478/awutm-2018-0007stirling’s methodlipschtiz continuity conditionmajorizing sequencessemilocal convergencelocal convergencecomputable radius of convergence |
| spellingShingle | Argyros Ioannis K. Parida P.K. Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions Annals of the West University of Timisoara: Mathematics and Computer Science stirling’s method lipschtiz continuity condition majorizing sequences semilocal convergence local convergence computable radius of convergence |
| title | Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions |
| title_full | Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions |
| title_fullStr | Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions |
| title_full_unstemmed | Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions |
| title_short | Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions |
| title_sort | expanding the applicability of stirling s method under weaker conditions and restricted convergence regions |
| topic | stirling’s method lipschtiz continuity condition majorizing sequences semilocal convergence local convergence computable radius of convergence |
| url | https://doi.org/10.2478/awutm-2018-0007 |
| work_keys_str_mv | AT argyrosioannisk expandingtheapplicabilityofstirlingsmethodunderweakerconditionsandrestrictedconvergenceregions AT paridapk expandingtheapplicabilityofstirlingsmethodunderweakerconditionsandrestrictedconvergenceregions |